An algorithm is proposed for training the single-layered perceptron. The algorithm follows successive steepest descent directions with respect to the perceptron cost function, taking care not to increase the number of misclassified patterns. The problem of finding these directions is stated as a quadratic programming task, to which a fast and effective solution is proposed. The resulting algori...

Active control methods have been applied to a number of practical problems in which it is necessary to control a tonal disturbance. For example, the control of engine noise and vibration in vehicles, propeller noise in aircraft and the vibration produced by reciprocating machinery in many industrial systems. In such applications the steepest-descent algorithm has been widely employed, in part d...

In recent years, there has been a series of results of Fokas and collaborators on boundary value problems for soliton equations (see [3] for a comprehensive review). The method of Fokas in [3] goes beyond existence and uniqueness. In fact, it reduces these problems to Riemann-Hilbert factorisation problems in the complex plane, thus generalising the existing theory which reduces initial value p...

We study the bias of generic optimization methods, including Mirror Descent, Natural Gradient Descent and Steepest Descent with respect to different potentials and norms, when optimizing underdetermined linear regression or separable linear classification problems. We ask the question of whether the global minimum (among the many possible global minima) reached by optimization can be characteri...